Place your prepared phyllo tart shells on a serving platter. Cut 24 small pieces (about 1 inch) from the wheel of brie cheese and place in phyllo tart shells. Cover and refrigerate any unused brie.
In a skillet over medium heat, melt the butter and add the asparagus, sautéing until asparagus has softened slightly. Season with salt and pepper to taste. Add a piece of asparagus to each phyllo tart shell on top of the brie.
Wipe pan clean and add 1 tbsp of olive oil over medium heat. Saute onions, stirring occasionally until they become softened and start to brown lightly (about 5 minutes). Add the brown sugar and balsamic vinegar and stir to coat the onions in the mixture. Spoon a teaspoon of the onion mixture into each phyllo tart shell. Serve the tarts warm* or at room temperature.
*if you would like to serve these tarts warm, you can place them on a baking sheet and warm them in the oven at 350 degrees F. for 5 to 7 minutes, or until cheese is melted.